A healthcare provider monitors the number of CAT scans performed each month in each of its clinics. The most recent year of data for a particular clinic follows (the reported variable is the number of CAT scans each month expressed as the number of CAT scans per thousand members of the health plan):
2.31, 2.09, 2.36, 1.95, 1.98, 2.25, 2.16, 2.07, 1.88, 1.94, 1.97, 2.02.
a. Find a 95% two-sided CI on the mean number of CAT scans performed each month at this clinic.
b. Historically, the mean number of scans performed by all clinics in the system has been 1.95. If there any evidence that this particular clinic performs more CAT scans on average than the overall system average?
Answers
Answer: a. 1.981 < μ < 2.18
b. Yes.
Step-by-step explanation:
A. For this sample, we will use t-distribution because we're estimating the standard deviation, i.e., we are calculating the standard deviation, and the sample is small, n = 12.
First, we calculate mean of the sample:
\(\overline{x}=\frac{\Sigma x}{n}\)
\(\overline{x}=\frac{2.31=2.09+...+1.97+2.02}{12}\)
\(\overline{x}=\) 2.08
Now, we estimate standard deviation:
\(s=\sqrt{\frac{\Sigma (x-\overline{x})^{2}}{n-1} }\)
\(s=\sqrt{\frac{(2.31-2.08)^{2}+...+(2.02-2.08)^{2}}{11} }\)
s = 0.1564
For t-score, we need to determine degree of freedom and \(\frac{\alpha}{2}\):
df = 12 - 1
df = 11
\(\alpha\) = 1 - 0.95
α = 0.05
\(\frac{\alpha}{2}=\) 0.025
Then, t-score is
\(t_{11,0.025}\) = 2.201
The interval will be
\(\overline{x}\) ± \(t.\frac{s}{\sqrt{n} }\)
2.08 ± \(2.201\frac{0.1564}{\sqrt{12} }\)
2.08 ± 0.099
The 95% two-sided CI on the mean is 1.981 < μ < 2.18.
B. We are 95% confident that the true population mean for this clinic is between 1.981 and 2.18. Since the mean number performed by all clinics has been 1.95, and this mean is less than the interval, there is evidence that this particular clinic performs more scans than the overall system average.
Related Questions
Put the following in order from the largest to the smallest.
Largest
114
0.2
60%
0.75
12
Answers
Answer:
11/4 0.75 60% 1/2 0.2
Step-by-step explanation:
Given
11/4 0.2 60% 0.75 1/2
Required
Order from largest to smallest
Convert all numbers to decimal
\(11/4 = 2.75\) ; \(60\% = 0.60\) and \(1/2 = 0.50\)
So, the numbers are:
2.75 0.2 0.60 0.75 0.50
From largest to least, we have:
2.75 0.75 0.60 0.50 0.2
Convert all numbers back to their original form
11/4 0.75 60% 1/2 0.2
12 is 40% of what number? (Hint: Divide) *
O
24
30
36
O 48
Answers
Answer:
B. 30
Step-by-step explanation:
Honestly I just looked it up
Answer:
30
Step-by-step explanation:
12÷ 40= 0.30
0.30= 30
A lawnmower was reduced in a sale by 2%. The new price is £127.40. What was the original cost of the lawnmower?
Answers
Answer:
130Step-by-step explanation:
A lawnmower was reduced in a sale by 2%. The new price is £127.40. What was the original cost of the lawnmower?
127.40 = 98%
127.40 : 98 * 100 = 130
-------------------
check
130 - 2% = 127.40
the answer is good
Answer:
130 pounds
Step-by-step explanation:
Let's say the original price was x, that'd mean x*0.98=127.40, x=127.4/0.98, x=130
If sum of first 6 digits of AP is 36 and that of the first 16 terms is 255,then find the sum of first ten terms.
•Please answer it correctly ( step by step)
Answers
Answer:
100
Step-by-step explanation:
We have the sum of first n terms of an AP,
Sn = n/2 [2a+(n−1)d]
Given,
36= 6/2 [2a+(6−1)d]
12=2a+5d ---------(1)
256= 16/2 [2a+(16−1)d]
32=2a+15d ---------(2)
Subtracting, (1) from (2)
32−12=2a+15d−(2a+5d)
20=10d ⟹d=2
Substituting for d in (1),
12=2a+5(2)=2(a+5)
6=a+5 ⟹a=1
∴ The sum of first 10 terms of an AP,
S10 = 10/2 [2(1)+(10−1)2]
S10 =5[2+18]
S10 =100
This is the sum of the first 10 terms.
Hope it will help.
\(\sf\underline{\underline{Question:}}\)
If sum of first 6 digits of AP is 36 and that of the first 16 terms is 255,then find the sum of first ten terms.
$\sf\underline{\underline{Solution:}}$
$\sf\bold\purple{||100||}$$\space$
$\sf\underline\bold\red{||Step-by-Step||}$
$\sf\bold{Given:}$
$\sf\bold{S6=36}$ $\sf\bold{S16=255}$$\space$
$\sf\bold{To\:find:}$
$\sf\bold{The \: sum\:of\:the\:first\:ten\:numbers}$$\space$
$\sf\bold{Formula\:we\:are\:using:}$
$\implies$ $\sf{ Sn=}$ $\sf\dfrac{N}{2}$ $\sf\small{[2a+(n-1)d]}$
$\space$
$\sf\bold{Substituting\:the\:values:}$
→ $\sf{S6=}$ $\sf\dfrac{6}{2}$ $\sf\small{[2a+(6-1)d]}$
→ $\sf{36 = 3[2a+(6-1)d]}$
→$\sf{12=[2a+5d]}$ $\sf\bold\purple{(First \: equation)}$
$\space$
$\sf\bold{Again,Substituting \: the\:values:}$
→ $\sf{S16}$ $\sf\dfrac{16}{2}$ $\sf\small{[2a+(16-1)d]}$
→ $\sf{255=8[2a + (16-1)d]}$
:: $\sf\dfrac{255}{8}$ $\sf\small{=31.89=32}$
→ $\sf{32=[2a+15d]}$ $\sf\bold\purple{(Second\:equation)}$
$\space$
$\sf\bold{Now,Solve \: equation \: 1 \:and \:2:}$
→ $\sf{10=20}$
→ $\sf{d=}$ $\sf\dfrac{20}{10}$ $\sf{=2}$
$\space$
$\sf\bold{Putting \: d=2\: in \:equation - 1:}$
→ $\sf{12=2a+5\times 2}$
→ $\sf{a = 1}$
$\space$
$\sf\bold{All\:of\:the\:above\:eq\: In \: S10\:formula:}$
$\mapsto$ $\sf{S10=}$ $\sf\dfrac{10}{2}$ $\sf\small{[2\times1+(10-1)d]}$
$\mapsto$ $\sf{5(2\times1+9\times2)}$
$\mapsto$ $\sf\bold\purple{5(2+18)=100}$
$\space$
$\sf\small\red{||Hence , the \: sum\: of \: the \: first\:10\: terms\: is\:100||}$
_____________________________
Identify the method that will be used to solve for x for each equation.
4x = 20
X - 11 = 9
5x + 6x = 22
5 (x - 2) = 30
Answers
Answer:
Identify the method that will be used to solve for x for each equation.
4x = 20
✔ division property of equality
x – 11 = 9
✔ addition property of equality
5x + 6x = 22
✔ combining like terms
5(x – 2) = 30
✔ distributive property
Step-by-step explanation:
HELP SOMEONE FOR 20 POINTS
Answers
You can also just use photo math
X= 2/5 and 8/3
which of these does NOT represent a polynomial when simplified??
Answers
Answer:
C
Step-by-step explanation:
Answer:
a.
Step-by-step explanation:
this was one of the problems you posted today, i'm sure a is the answer (:
Question 7(Multiple Choice Worth 5 points)
(Scale Factor MC)
Ascale drawing of a famous statue uses a scale factor of 260:1. If the height of the drawing is 1.2 feet, what is the actual height of the statue?
O261 2 feet
0312.0 feet
O216.7 feet
O258.8 feet
Answers
The actual height of the statue is 0312.0 feet. Since the scale factor is 260/1.
What is meaning height?
Height, altitude, and elevation all refer to the vertical distance between something's top and bottom or its base and something above it. Height is used to describe everything that may be measured vertically, high or low.
Given that to draw a drawing the painter use the scale factor 260:1. It means if the height of a statue in the drawing is 1 unit then the actual height of the statue will be 260.
The height of a statue in the drawing is 1.2 feet.
Assume that the height of the statue be x feet.
Therefore,
x/1.2 = 260/1
x/1.2 = 260
Multiply both sides by 1.2:
x = 260 × 1.2
x = 312
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The correct option is B, 312.0
find the vertex of f(x)=5x^2+40x-3
Answers
From the question given:
f(x) = 5x² + 40x - 3
comparing the above with ax² + bx + c
a = 5
b = 40
c=-3
The x - axis of the vertex can be gotten by simply finding the value of -b/2a
\(x=\frac{-b}{2a}\)\(=\frac{-10}{2(5)}=\frac{-40}{10}=\text{ -}4\)To get the y-axis of the vertex, simply substitute the value of x=-4 into the function given
That is ;
\(f(-1)=5(-4)^2+\text{ 40(-4) - 3}\)\(=5(16)\text{ - 160 - 3}\)\(=80\text{ - 160 - 3}\)\(=\text{ -83}\)The function has a vertex at: (-4, -83)
Bags of sugar come in 3 sizes.
Small bag: A 175 g bag costs 55p.
Medium bag: A 525 g bag costs £1.76.
Large bag: A 1.15 kg bag costs £3.51.
Find the cost per gram for each bag of sugar.
Round your answers to 3dp.
Answers
Answer:
The cost per gram for each bag is:
Small bag: 0.00314 £
Medium bag: 0.00335 £
Large bag: 0.00305 £
Step-by-step explanation:
Small bag:
If 175 g cost 0.55 £, 1 g will be:
\( \frac{1g*0.55 \£}{175\: g} = 0.00314 \£\)
Medium bag:
If 525 g cost £ 1.76, 1g will be:
\( \frac{1g*1.76 \£}{525\: g} = 0.00335 \£\)
Large bag:
If 1150 g cost £ 3.51, 1g will be:
\( \frac{1g*3.51 \£}{1150\: g} = 0.00305 \£\)
I hope it helps you!
Solve by Factoring:
2x^2 - x - 3 = 0
Answers
Answer:
x = 3/2 or x = -1
Step-by-step explanation:
2x² - x - 3 = 0
2*(-3) = -6
Factors of -6:
(-1, 6), (1, -6), (-2, 3), (2, -3)
We need to find a pair that adds up to the co-eff of x which is (-1)
Factors :(2,-3)
2 - 3 = -1
so, 2x² - x - 3 = 0 can be written as:
2x² + 2x - 3x - 3 = 0
⇒ 2x(x + 1) -3(x + 1) = 0
⇒ (2x - 3)(x + 1) = 0
⇒ 2x - 3 = 0 or
x + 1 = 0
⇒ 2x = 3 or x = -1
⇒ x = 3/2 or x = -1
what is the value of x? ill give brainiest
Answers
The value of x is 23.
Consider a function f defined as follows: f(x)=(x-3)^2, x belongs to [1,2]. Is f invertible in the domain [1,2]? If yes, find the inverse of the function.
(Looking for an complete explanation on how to prove invertible, probably by showing the function is one-to-one and then determining the inverse. )
Answers
The inverse of the function is f⁻¹(x)=3+√18+x, 3-√18+x
What is a function?A relation is a function if it has only One y-value for each x-value.
Let us consider the function f(x)=(x-3)²
Where x belongs to [1, 2]
f(x)=x²+9-6x
y=x²+9-6x
Interchange the variables.
x=y²+9-6y
y=3+√18+x
y=3-√18+x
Relace y with f⁻¹(x)
f⁻¹(x)=3+√18+x, 3-√18+x
Hence, the inverse of the function is f⁻¹(x)=3+√18+x, 3-√18+x
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What is the range of y=1/3x
Answers
Answer:
all real numbers
Step-by-step explanation:
you can create any value for y with a value for x, hence the range is "everything".
Answer:
All real numbers
Step-by-step explanation:
help pls pls pls pls pls pls pls pls
Answers
30-60-90 triangle question is in the image
Answers
Answer:
it is easy 56 and 45 and 567
How to divide decimals by decimals that the decimals has different place values
Answers
When multiplying decimals, the number of decimal places in the product is the sum of the decimal places in the factors. When dividing by decimals, move the decimal point in the dividend the same number of places to the right as you move the decimal point in the divisor.
Ayuda operaciones y respuesta es para ahora
Answers
The perimeter of the given window is 48 centimeter.
From the given figure,
Perimeter of window = 2(Length+Breadth)
= 2(10+14)
= 2×24
= 48 centimeter
Perimeter of house = 2(Length+Breadth)
= 2(37+35)
= 2×72
= 144 centimeter
Perimeter of roof = 2(Length+Breadth)
= 2(37+5)
= 2×42
= 84 centimeter
Therefore, the perimeter of the given window is 48 centimeter.
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Please help me with this question please
Answers
\({ \qquad\qquad\huge\underline{{\sf Answer}}} \)
The pair of opposite angles formed by two intersecting straight lines are known as Vertical Angles.
In the given figure, there are two pairs of vertical angles~
That are :
\(\qquad \sf \dashrightarrow \: \angle1 \: \: and \: \: \angle3\)
and
\(\qquad \sf \dashrightarrow \: \angle2 \: \: and \: \: \angle4\)
Also, vertical opposite angles are equal in measure.
Solve the equation p + 19 = 51
Answers
Answer:
p=32
Step-by-step explanation:
Answer:
Step-by-step explanation:
p+19=51
p=51-19
p=32
At a sale this week, a desk is being sold for $536. This is 67% of the original price.
What is the original price?
Answers
Answer:
884.4
Step-by-step explanation:
Answer:
The original price is 895.12$
I haven't done percent in ages, lmk if you get it right
kudos to any other answer besides this
Step-by-step explanation:
Translate the sentence into an equation.
Twice the difference of a number 2 and equals 9.
Answers
Hope this helps !! have a good day
Can I please get some help I’ve been stuck on this question for a while!
Answers
Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes
How many minutes of the ride are spent higher than 28 meters above the ground?The radius of the Ferris wheel is 30 / 2 = 15 meters.
The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.
The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.
The angle between these two positions is 180 degrees.
The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.
Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.
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Come on a survey of 500 farmer show that other farmers 125 grow only be one07 grow only corn 87 crew only old 200 Route 59 grow wheat and corn 50 groovy and old and 176 grill corn determine the number of farmers whole group at least one of the three grew all three did not grow any of the three and 4 exactly 2 of the three
Answers
The number of farmers who grew at least one of the three crops is 921
Let's analyze the given information step by step to determine the number of farmers who grew at least one of the three crops, the number of farmers who did not grow any of the three crops, and the number of farmers who grew exactly two of the three crops.
According to the survey results:
125 farmers grow only beans.
107 farmers grow only corn.
87 farmers grow only old.
200 farmers grow wheat and corn.
50 farmers grow wheat and old.
176 farmers grow corn.
To find the number of farmers who grew at least one of the three crops, we need to sum up the number of farmers who grew each crop individually and subtract the number of farmers who grew both combinations of crops:
Number of farmers who grew beans = 125
Number of farmers who grew corn = 107 + 200 + 176 = 483
Number of farmers who grew old = 87 + 50 + 176 = 313
Adding these numbers, we get:
125 + 483 + 313 = 921
Therefore, 921 farmers grew at least one of the three crops.
To find the number of farmers who did not grow any of the three crops, we subtract the total number of farmers in the survey from the number of farmers who grew at least one of the three crops:
500 - 921 = -421
Since we can't have a negative number of farmers, we can conclude that there is an error in the given information.
As for the number of farmers who grew exactly two of the three crops (beans, corn, or old), we don't have enough information to determine this value based on the given data.
In conclusion, the number of farmers who grew at least one of the three crops is 921 (assuming there was an error in the given information). The number of farmers who did not grow any of the three crops cannot be determined with the information provided, and the number of farmers who grew exactly two of the three crops cannot be determined.
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What is the equivalent expression of 3x^2-4x-3
Answers
Answer:
C. 3(x+1)(x-1)-4x
Step-by-step explanation:
3(x+1)(x-1)-4x
(x+1)(x-1)=x^2-1
3(x^2-1)-4x
3x^2-4x-3
Alexander is collecting aluminum cans for charity. One empty 355 ml can weighs about 17 g. It takes 59 cans to get about 1 kg of 100% recyclable aluminum.
Over one month, he collected 1297 cans.
What is the mass, in kilograms, of these cans?
Answers
Answer:
22 kg
Step-by-step explanation:
1297 cans * (17 grams)/(1 can) * (1 kg)/(1000 g) = 22.049 kg
Answer: 22 kg
3 over 4 of 4 over 5 ?
Answers
Answer:
what's the question? it could be both
Giving brainliest!!!!!
Answers
6 x 10 x 5 = 300
4/3 x π x r x 4³ = 268.08257310633
268.08257310633 + 300 = 434.041286553
Answer:
434 \(cm^3\)
Step-by-step explanation:
volume of bottom: 6 x 10 x 5 = 300 \(cm^3\)
volume of top:
\(V = (\frac{4}{3}\pi r^3)/2\\\\= (\frac{4}{3}\pi(4)^3)/2\\\)
≈ 134.041 \(cm^3\)
300 + 134.041 = 434.041
they want to the nearest tenth, so it would just be 434.0
I really need help i keep getting confused
Answers
Answer:
funny half done find find
(PLEASE OPEN) Need help with triangle proofs, please.
Answers
The triangle proof that shows that angle Q and angle S are congruent to each other is explained below.
What is the Side-angle-side Congruence Theorem (SAS)?The side-angle-side congruence theorem (SAS) states that if the two sides and an included angle in one triangle is congruent to two corresponding sides and an included angle in the other triangle, then both triangles are congruent to each other.
If two triangles are congruent to each other, the CPCTC theorem states that all their corresponding parts are also equal or congruent to each other.
The triangle proof is given as:
Statements Reasons
1. PR bisects ∠PQS 1. Given
2. ∠1 ≅ ∠2 2. Definition of bisection
3. PQ ≅ PS 3. Given
4. RP ≅ PR 4. Reflexive property
5. ΔQPR ≅ ΔSPR 5. SAS theorem
6. ∠Q ≅ ∠S 6. CPCTC
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